Help! Hen can't stand up still alert and eating but green poo

My 1 1/2 yr old Barred rock hen is sick. She has been losing feathers on her back for about 2 months (thought it was the rooster because it was just on her back. She was laying and doing just fine but I have noticed a slight decrease in egg production over the last couple weeks. 2 days ago she came staggering into the run to get a drink of water and just plopped down to drink. I let all of the chickens out and she staggered out to free range but didn't really go anywhere, just laid down. Yesterday I got a kennel from my friend to separate her and chased her around for a few minutes. She can run a bit but after a minute just gave up. She squats like she is sitting on eggs or lays on her side with her wing out to balance. Yesterday I noticed that her poo is greenish yellow, more green though. Its really runny and stuck all over her feathers but her vent is clear. She looks a little skinny but not bad. She is pecking around in her shavings and ate some scratch I threw in there to see if she was still eating (she keeps spilling her food so I don't know if she is eating that.) I bought some Rooster Booster vitamin and electrolyte for her water. I also got baby vitamins and tried to give those with a syringe but she just shook her beak and would only take a few drops. I put the remainder of the dose in her water as well. She seems alert and looks happy just sitting there but she still has some paralysis in her legs and maybe one wing.

As a side note, about a month ago I lost another hen. They ran out of water when I had to leave town for an emergency and when I got back she was curled up in a ball with her head turned around, she made a weird noise had heavy breathing and died before I could get in there. I attributed it to her running out of water and being lowest on the pecking order (but they were only out of water for a day and it was hot about 100). She had also lost feathers on her back about 2 months before that. I had a rooster with just 4 hens so I was pretty sure it was due to that, I was just waiting for the babies to get bigger to put with them so he would have more selection

Not sure if it is related. These were our favorite hens and most friendly so I am really hoping to save this one. Should I go ahead and pick up some antibiotics and put it in there just in case? I ordered the Rooster Booster worming stuff to put on their food but have not wormed before. None of the other chickens have lost feathers and seem just fine. We also had some more babies hatch in the coop yesterday so really hoping its not contagious to them, but I don't have anywhere to separate them to. Due to recent coyote attacks and losing the hen our flock is down to 8 plus the babies (I have seen one so far but she is sitting on 5 eggs). I hope we don't lose anymore!

Any help is appreciated. I have been googling for 2 days, searching threads on here and everywhere. I don't think its Mareks, she doesn't seem to have discharge but has made a slight rattle noise once that I heard so can't rule out respiratory, the poo could be just from her not eating enough, the paralysis seems like it could be fungal or bacterial but the treatments are different. I don't know which direction to go.